{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:LZZTX2HLMG5RHPTMKB55J4UPQA","short_pith_number":"pith:LZZTX2HL","canonical_record":{"source":{"id":"1701.05817","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-01-20T15:07:02Z","cross_cats_sorted":[],"title_canon_sha256":"882c8fa9de3079485bb028e9b60e28416d9f44dbc1851c13fd277666f4ad91a4","abstract_canon_sha256":"2a8fdf1d4f3d89c49236e0ba715508016a611d84544e22b5c775ae72a7b1dd7d"},"schema_version":"1.0"},"canonical_sha256":"5e733be8eb61bb13be6c507bd4f28f8033bda9cd398bcf7831e36c562ca5ba61","source":{"kind":"arxiv","id":"1701.05817","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.05817","created_at":"2026-05-18T00:52:24Z"},{"alias_kind":"arxiv_version","alias_value":"1701.05817v1","created_at":"2026-05-18T00:52:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.05817","created_at":"2026-05-18T00:52:24Z"},{"alias_kind":"pith_short_12","alias_value":"LZZTX2HLMG5R","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_16","alias_value":"LZZTX2HLMG5RHPTM","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_8","alias_value":"LZZTX2HL","created_at":"2026-05-18T12:31:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:LZZTX2HLMG5RHPTMKB55J4UPQA","target":"record","payload":{"canonical_record":{"source":{"id":"1701.05817","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-01-20T15:07:02Z","cross_cats_sorted":[],"title_canon_sha256":"882c8fa9de3079485bb028e9b60e28416d9f44dbc1851c13fd277666f4ad91a4","abstract_canon_sha256":"2a8fdf1d4f3d89c49236e0ba715508016a611d84544e22b5c775ae72a7b1dd7d"},"schema_version":"1.0"},"canonical_sha256":"5e733be8eb61bb13be6c507bd4f28f8033bda9cd398bcf7831e36c562ca5ba61","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:52:24.646032Z","signature_b64":"qDsax34/ZQdrOnPX/hKwMeklFBNRUvifA0bqlfcfrpGT3PqxgVqenH+FktghPgsp5J5zvSLC9XVzlLZgc6D8BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5e733be8eb61bb13be6c507bd4f28f8033bda9cd398bcf7831e36c562ca5ba61","last_reissued_at":"2026-05-18T00:52:24.645267Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:52:24.645267Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1701.05817","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:52:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O4eIcxKgwl94C517Yx7FASUI5X3HkosazeweTjnQOpIF/CRWAPJnU/Lk6Z3+HoCZRk30nM38AlZso919MEbZDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T20:51:23.177434Z"},"content_sha256":"e09e4009d0852e84d3a43dc5313134c3a25dc96ef60418989a36b8c97a8471d2","schema_version":"1.0","event_id":"sha256:e09e4009d0852e84d3a43dc5313134c3a25dc96ef60418989a36b8c97a8471d2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:LZZTX2HLMG5RHPTMKB55J4UPQA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Uniformly rational varieties with torus action","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Alvaro Liendo, Charlie Petitjean","submitted_at":"2017-01-20T15:07:02Z","abstract_excerpt":"A smooth variety is called uniformly rational if every point admits a Zariski open neighborhood isomorphic to a Zariski open subset of the affine space. In this note we show that every smooth and rational affine variety endowed with an algebraic torus action such that the algebraic quotient has dimension 0 or 1 is uniformly rational."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.05817","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:52:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RWJQe/EWMBsXGxutqCOfGMEFoWcDy2bEvcfIAhC+5vgBER32ti8Jut2Ebu3s+pznTw2Tc2c/K75Ki4DFktKlAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T20:51:23.177771Z"},"content_sha256":"337f5f7252632d52c9233bea5cce27419a56b1f81c40a4213a63bb491fddb4a6","schema_version":"1.0","event_id":"sha256:337f5f7252632d52c9233bea5cce27419a56b1f81c40a4213a63bb491fddb4a6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LZZTX2HLMG5RHPTMKB55J4UPQA/bundle.json","state_url":"https://pith.science/pith/LZZTX2HLMG5RHPTMKB55J4UPQA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LZZTX2HLMG5RHPTMKB55J4UPQA/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-21T20:51:23Z","links":{"resolver":"https://pith.science/pith/LZZTX2HLMG5RHPTMKB55J4UPQA","bundle":"https://pith.science/pith/LZZTX2HLMG5RHPTMKB55J4UPQA/bundle.json","state":"https://pith.science/pith/LZZTX2HLMG5RHPTMKB55J4UPQA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LZZTX2HLMG5RHPTMKB55J4UPQA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:LZZTX2HLMG5RHPTMKB55J4UPQA","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"2a8fdf1d4f3d89c49236e0ba715508016a611d84544e22b5c775ae72a7b1dd7d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-01-20T15:07:02Z","title_canon_sha256":"882c8fa9de3079485bb028e9b60e28416d9f44dbc1851c13fd277666f4ad91a4"},"schema_version":"1.0","source":{"id":"1701.05817","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.05817","created_at":"2026-05-18T00:52:24Z"},{"alias_kind":"arxiv_version","alias_value":"1701.05817v1","created_at":"2026-05-18T00:52:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.05817","created_at":"2026-05-18T00:52:24Z"},{"alias_kind":"pith_short_12","alias_value":"LZZTX2HLMG5R","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_16","alias_value":"LZZTX2HLMG5RHPTM","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_8","alias_value":"LZZTX2HL","created_at":"2026-05-18T12:31:28Z"}],"graph_snapshots":[{"event_id":"sha256:337f5f7252632d52c9233bea5cce27419a56b1f81c40a4213a63bb491fddb4a6","target":"graph","created_at":"2026-05-18T00:52:24Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"A smooth variety is called uniformly rational if every point admits a Zariski open neighborhood isomorphic to a Zariski open subset of the affine space. In this note we show that every smooth and rational affine variety endowed with an algebraic torus action such that the algebraic quotient has dimension 0 or 1 is uniformly rational.","authors_text":"Alvaro Liendo, Charlie Petitjean","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-01-20T15:07:02Z","title":"Uniformly rational varieties with torus action"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.05817","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:e09e4009d0852e84d3a43dc5313134c3a25dc96ef60418989a36b8c97a8471d2","target":"record","created_at":"2026-05-18T00:52:24Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"2a8fdf1d4f3d89c49236e0ba715508016a611d84544e22b5c775ae72a7b1dd7d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-01-20T15:07:02Z","title_canon_sha256":"882c8fa9de3079485bb028e9b60e28416d9f44dbc1851c13fd277666f4ad91a4"},"schema_version":"1.0","source":{"id":"1701.05817","kind":"arxiv","version":1}},"canonical_sha256":"5e733be8eb61bb13be6c507bd4f28f8033bda9cd398bcf7831e36c562ca5ba61","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5e733be8eb61bb13be6c507bd4f28f8033bda9cd398bcf7831e36c562ca5ba61","first_computed_at":"2026-05-18T00:52:24.645267Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:52:24.645267Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qDsax34/ZQdrOnPX/hKwMeklFBNRUvifA0bqlfcfrpGT3PqxgVqenH+FktghPgsp5J5zvSLC9XVzlLZgc6D8BA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:52:24.646032Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.05817","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e09e4009d0852e84d3a43dc5313134c3a25dc96ef60418989a36b8c97a8471d2","sha256:337f5f7252632d52c9233bea5cce27419a56b1f81c40a4213a63bb491fddb4a6"],"state_sha256":"a8397834e9218236f09b4dd8a3639115892eb5fa000b42fe8c3edbeb37b180bd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iykG6ZFU0BvBT4AvKNBR0G7uZfGyycD1g0O0BNF2KFK2M4jDcbSqbXuFQIP2VaJ+uLLqwBSQFIJeI8eU8gpdAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T20:51:23.179685Z","bundle_sha256":"dc798dc60f9177c987861ea9071fc0c87aa7b6fc67932a4c06da73d7c19ecd55"}}